Question

express the equation x+3y=-6 in slope-intercept form

Answer 1

To express the equation \( x + 3y = -6 \) in slope-intercept form, we want to solve for \( y \) in terms of \( x \). The slope-intercept form is given by the formula:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

Starting with the given equation:

\[
x + 3y = -6
\]

1. Subtract \( x \) from both sides:

\[
3y = -x - 6
\]

2. Now, divide every term by 3 to solve for \( y \):

\[
y = -\frac{1}{3}x - 2
\]

Now the equation is in slope-intercept form \( y = mx + b \) where \( m = -\frac{1}{3} \) and \( b = -2 \).

Thus, the equation in slope-intercept form is:

\[
y = -\frac{1}{3}x - 2
\]